The nucleon as a test case to calculate vector-isovector form factors at low energies

Abstract

Extending a recent suggestion for hyperon form factors to the nucleon case, dispersion theory is used to relate the low-energy vector-isovector form factors of the nucleon to the pion vector form factor. The additionally required input, i.e. the pion-nucleon scattering amplitudes are determined from relativistic next-to-leading-order (NLO) baryon chiral perturbation theory including the nucleons and optionally the Delta baryons. Two methods how to include pion rescattering are compared: (a) solving the Muskhelishvili-Omnes (MO) equation and (b) using an N/D approach. It turns out that the results differ strongly from each other. Furthermore the results are compared to a fully dispersive calculation of the (subthreshold) pion-nucleon amplitudes based on Roy-Steiner (RS) equations. In full agreement with the findings from the hyperon sector it turns out that the inclusion of Delta baryons is not an option but a necessity to obtain reasonable results. The magnetic isovector form factor depends strongly on a low-energy constant of the NLO Lagrangian. If it is adjusted such that the corresponding magnetic radius is reproduced, then the results for the corresponding pion-nucleon scattering amplitude (based on the MO equation) agree very well with the RS results. Also in the electric sector the Delta degrees of freedom are needed to obtain the correct order of magnitude for the isovector charge and the corresponding electric radius. Yet quantitative agreement is not achieved. If the subtraction constant that appears in the solution of the MO equation is not taken from nucleon+Delta chiral perturbation theory but adjusted such that the electric radius is reproduced, then one obtains also in this sector a pion-nucleon scattering amplitude that agrees well with the RS results.

12 pages, discussion and references added, results unchanged

References in corpus (9)

• The pion-pion scattering amplitude. IV: Improved analysis with once subtracted Roy-like equations up to 1100 MeV
• Electromagnetic excitation of the Delta(1232)-resonance
• The Proton Radius Puzzle
• Dispersive analysis of the pion transition form factor
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• Anomalous decay and scattering processes of the eta meson
• The electromagnetic Sigma-to-Lambda hyperon transition form factors at low energies
• Peripheral transverse densities of the baryon octet from chiral effective field theory and dispersion analysis

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• Systematic calculations of cluster radioactivity half-lives with a screened electrostatic barrier
• Chiral constraints on the isoscalar electromagnetic spectral functions of the nucleon from leading order vector meson couplings
• Calculation of true coincidence summing correction factor for a Broad Energy Germanium (BEGe) detector using standard and fabricated sources
• Confronting Dual Models of the Strong Interaction
• Tidal deformability of neutron stars with exotic particles within a density dependent relativistic mean field model in R-squared gravity
• A Novel Regularization Scheme for Nucleon-Nucleon Lattice Simulations with Effective Field Theory
• Dispersive Analysis of $D$- and $B$-Meson Form Factors with Chiral and Heavy-Quark Constraints
• Electromagnetic transition form factors and Dalitz decays of hyperons